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Using properties of determinants. Prove ...

Using properties of determinants. Prove that`|[1 ,1+p,1+p+q],[2, 3+2p,4+3p+2q],[3, 6+3p, 10+6p+3q]|=1`

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To prove that \[ D = \begin{vmatrix} 1 & 1+p & 1+p+q \\ 2 & 3+2p & 4+3p+2q \\ 3 & 6+3p & 10+6p+3q \end{vmatrix} = 1, ...
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Using properties of determinants, prove the following: |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=1

Show that: |[1 ,1+p,1+p+q],[2, 3+2p,1+3p+2q],[3, 6+3p,1+6p+3q]|=1 .

Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=1

Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]| = 1

Show that |(1, 1+p, 1+p+q), (2, 3+2p, 4+3p+2q), (3, 6+3p, 10+6p+3q)|=1.

Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

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NCERT ENGLISH-DETERMINANTS-All Questions
  1. Solve the system of equations2/x+3/y+(10)/z=4,4/x-6/y+5/z=1,6/x+9/y-(2...

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  2. Using properties of determinants. Prove that |(sinalpha,cosalpha,cos(a...

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  3. Using properties of determinants. Prove that|[1 ,1+p,1+p+q],[2, 3+2p,4...

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  4. Using properties of determinants. Prove that|[3a,-a+b,-a+c],[-b+a,3b,-...

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  5. Using properties of determinants, prove the following: |xx^2 1+p x...

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  6. Using properties of determinants. Prove that|(alpha,alpha^2,beta+gamma...

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  7. Evaluate |[1,x, y],[1,x+y, y],[1,x,x+y]|

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  8. Write Minors and Cofactors of the elements of following determinants:...

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  9. Using Cofactors of elements of second row, evaluate Delta=|(5, 3, 8),(...

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  10. Write Minors and Cofactors of the elements of following determinants:...

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  11. If Delta=|[a(11),a(12),a(13)],[a(21),a(22),a(23)],[a(31),a(32),a(33)]|...

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  12. Using Cofactors of elements of third column, evaluate Delta=|(1,x, y ...

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  13. Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

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  14. EvaluateDelta=|1a b c1b c a1c a b|

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  15. Show that |a b c a+2x b+2y c+2z x y z|=0

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  16. Prove that |a a+b a+b+c2a3a+2B4a+3b+2c3a6a+3b 10 a+6b+3c|=a^3

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  17. Show that|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc(1+1/a+1/b+1/c)=abc+bc+ca+...

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  18. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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  19. Prove: |[b+c,a,a],[b,c+a,b],[c,c,a+b]|=4a b c

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  20. If x, y, z are different and Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=...

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